Free and Open Source Software

Unless your initial recordings were lossless (they probably weren’t), recompressing the files with a lossless flag will only increase the size by a lot. Lossless video is HUGE, which is why almost no one actually records/saves it. What you’re probably looking for is visually lossless transcoding, where you do lose some data, but the difference is too small for most people to notice.

My recommendations:

1. Go to your recording software and change the setting to better compress your videos the first time around. Compressing once generally gives a better quality to size ratio than compressing twice. It’s therefore best if your recording software get it right first time, without you having to keep on recompressing your videos.
2. When tinkering with encoding setting, trying to find what works best for you, it might be useful to install Identity to help you compare the original files and one or more transcoded version(s).
3. Don’t try to recompress the audio; you’ll save very little space, and the losses in quality become perceptible much faster than video. When using ffmpeg, the “-c:a copy” flag should simply copy the original audio to the new file, without any change in quality or size
4. I’d recommend taking some time to read through the ffmpeg encoding guides. H265 and AV1 are good for personal archiving, with AV1 providing better compression ratios at the cost of much slower encoding. You could also choose VP9, which is similar in compression ratio and encoding speed to h265.
5. You’ll have to choose between hardware and software encoding. Hardware encoding can (depending on your specific hardware and settings) be 10-100x faster than software, but software generally gives better compression ratios at similar qualities. You should test this difference for yourself and see if the extra time is worth it for the extra quality. Do keep in mind that AV1 hardware encoding is only supported by some of the most recent GPU’s (rx7000 and rtx4000 from the top of my head). If you don’t have one of those GPU’s, you’ll either have to choose software encoding or pick a different codec.

"Lossless" isn't the term you want; that refers to not lossily compressing the main data. Lossless compression or storage of media is very rare outside of text and sometimes audio, because it ends up so large.

You want to preserve metadata. That applies regardless of how lossy the data compression is.

I don't think it's possible, or at least not in the way you're thinking. Encoding a video with lossless flags usually results in a file size bigger or about the same as the source, and on top of that it takes a long time to actually do the encode.

Video is already highly compressed.

But for sure you can tinker around with ffmpeg (FOSS) & see how it goes for you. I've done it in the past just for kicks since some of the common video codec encoders do have lossless flags but it really wasn't worth the effort.

EDIT: That's just the video in the file, you also have to contend with the audio. That's a bit easier if you just want to use ffmpeg to dump everything into FLAC but again, I don't think you're saving much hard drive space if any.

Ffmpeg

FFmpeg has FFV1 which is lossless

I'd suggest using IFME (https://x265.github.io/download.html) it does support MKV.

Due to the nature of video, using another codec will have some differences even if it's minimal.

But if you encode the video as AV1 with conservative settings it should be possible to reclaim a lot of that space with minimal impact.

Metadata should be retainable but you'll likely need to experiment.